Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3^+ Cluster

The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method of a modified arrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a. u at R = 1.55 a(0). The binding energy of He-3(+) with respect to He+He++He was calculated to be 0.1064 a.u. (about 2.89 eV). This means that the He-3(+) cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two helium atoms.

Planar System-Masses in an Equilateral Triangle:Numerical Study within Fractional Calculus

In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its classical Lagrangian.Secondly,the classical Euler-Lagrange equations(i.e.,the classical equations of motion)are derived.Thirdly,we fractionalize the classical Lagrangian of the system,and as a result,we obtain the fractional Euler-Lagrange equations.As the final step,we give the numerical simulations of the fractional model,a new model which is based on Caputo fractional derivative.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3+ Cluster

The formation mechanism for the equilateral triangle structure of the He3+ cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3+ with respect to He+He+ +He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3+ cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two heliumatoms.

Resonant Length Formulations for Dual Band Slot Cut Equilateral Triangular Microstrip Antennas

The dual band equilateral triangular microstrip antennas are realized by cutting the slots of either quarter wave or half wave in length, inside the patch. In this design, however these simpler approximations of slot length against the frequency do not give closer results for different slot lengths and there positions inside the patch. In this paper, the modal variations of slot cut patch antennas over wide frequency range are studied. It is observed that the slot does not introduce any mode but reduces the higher order mode resonance frequency of the patch and along with the fundamental mode realizes dual band response. The formulations of the resonant length for the mode introduce by the slots in these antennas are proposed. The resonance frequencies calculated using proposed formulations agree well with the simulated results with an error of less than 5%.

NATURAL SUPERCONVERGENT POINTS OF EQUILATERAL TRIANGULAR FINITE ELEMENTS - A NUMERICAL EXAMPLE

A numerical test case demonstrates that the Lobatto and the Gauss points are not natural superconvergent points of the cubic and the quartic finite elements under equilateral triangular mesh for the Poisson equation.

Study of Mode Characteristics for Equilateral Triangle Semiconductor Microlasers

InGaAsP semiconductor ETR microlasers with side length of 5 and 10 um are fabricated by ICP etching. The peaks in photoluminenscent spectra corresponding to longitudinal modes are observed with the interval consisting with the theoretical formulae.

Experimental Study on the Penetration of Diesel and Biodiesel Spray Liquid Emerging from an Equilateral Triangular Orifice under Evaporative Conditions

This paper reports the results of an experimental study on the liquid phase characteristics of the biodiesel and diesel discharged from an equilateral triangular orifice and a circular orifice under different injection conditions by Mie-scattering imaging.The results revealed that the biodiesel liquid penetration length was longer than that of diesel under the same injection conditions.In addition,the increase of the chamber pressure was expected to enhance the interaction between air and fuel,resulting in the acceleration of the liquid phase breakup process.Moreover,with increasing chamber temperature,the liquid penetration of biodiesel was reduced less than that of diesel.This was due to the high surface tension and viscosity of biodiesel which inhibited the chamber air entrainment and suppressed the liquid breakup process.Accordingly,the higher probability of shorter diesel liquid penetration length indicated better air-fuel mixing than that of biodiesel.Besides,the triangular orifice liquid length was shorter than that of the circular orifice.And the stabilized liquid cone angle from the circular orifice was larger than that from the triangular orifice,indicating that using an equilateral triangular orifice has the potential to improve the air-fuel mixing process.

Semiclassical Analysis of Quarter Stadium Billiards

An expansion method for stationary states is applied to obtain the eigenfunctions and the eigenenergies of the quarter stadium billiard, and its nearest energy-level spacing distribution is obtained. The histogram is consistent with the standard Wigner distribution, which indicates that the stadium billiard system is chaotic. Particular attention is paid to pursuing the quantum manifestations of such classical chaos. The correspondences between the Fourier transformation of quantum spectra and classical orbits are investigated by using the closed-orbit theory. The analytical and numerical results are in agreement with the required resolution, which corroborates that the semiclassical method provides a physically meaningful image to understand such chaotic systems.

架空输电线路三相导线间安培力分析

研究输电导线的舞动及仿真时,需要计及多种激励因素。在不同传输功率时,导线电流产生的安培力在导线舞动仿真中是否计及、如何计及等问题需要回答。从基本电磁场理论出发,推导了通用输电线安培力计算表达式、画出了安培力随时间变化的轨迹图。由于导线质量较大、安培力较小且其方向与大小随电网频率相同、导线舞动频率与电网电流频率相比很低,对导线舞动的激励可以忽略,在仿真计算中不计及其作用。

Compact Two Shorting Pin Loaded ETMA

In this study ETMA （Equilateral Triangular Microstrip Antennas） are designed to form dual frequency by inserting two shorting pins. Microstrip patch antennas＇ resonant frequencies with two shorting pins are represented in this study by not only considering the theoretical results but also considering the both simulated and experimental results. For each geometry, positions of shorting pins are varied and effects of these variations are analyzed. The presented patch antennas in literature which have the same shape with shorting pin and without shorting pin are compared and results are presented. The methods in literature presented for estimating the resonant frequency depends on analytical methods which are originated from curve fitting. The results of this study will be the basement of the latter studies that predict the resonant frequencies of mentioned antennas before producing the antenna so that the engineers handle the problem by saving the time and estimating the frequency before production.

A New Critical Value Concerning the Genealogy of Long Period Families at L_4 in the Restricted Three-body Problem

We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.

Geometric characterizations for variational minimization solutions of the 3-body problem

For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.

Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular rostricted 3-body problem in R^3 or R^2 are also planar equilateral triangle circular solutions.